Was bedeutet Israeli Prime Minister Benjamin Netanyahu will make a televised announcement Monday evening in what his office said would disclose "dramatic news" regarding the nuclear agreement with Iran ?

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This sentence is actually wrong; it isn't good English. The subject of "would disclose" is the announcement. The announcement would disclose dramatic news. However, "in what" does not make sense here.

Here is an example where "in what" is used correctly:

"Trump has agreed to meet with Kim Jong Un in what would be the first meeting between a U.S. president and North Koreans."

"In what" is always used with some form of "to be". In what would be / in what will be / in what could become... etc. It is a way of mentioning an event and then explaining the significance of the event. The part that comes after "in what" tells us why the event was worth talking about.

It should not be in the sentence you read, though.